Download Structure of HSNP Numeracy - Four levels of proficiency

Multiplication 5:
2-3- and 4-digit numbers using
written algorithm and fractions
Objectives

Use the grid method to multiply two-digit numbers by two and
three-digit numbers

Use a written method to multiply three and four-digit numbers by
single-digit numbers, including decimals. NB Some teachers may
prefer to stick to the grid method rather than doing the written
algorithm. If so, repeat Day 1 – making it last two days.

Multiply pairs of fractions
For this unit you will need:
playing cards, Grid method at
http://www.topmarks.co.uk/Flash.aspx?f=gridmethodpvcardsv3
Watch out for pupils who:

do not know their times tables. This lack of knowledge will really
slow down their work in multiplication and division so use Term 2
weeks 4 and 9 day 1’s activities with tables as necessary;

struggle with place value when multiplying decimals, e.g. think
that 4 × 0.3 = 0.12; they may find it helpful to practice counting up
in steps of 0.3 or 0.03 for example;

do not realise that to find half of a fraction for example is the same
as multiplying a fraction by one half.
HSNP © Hamilton 2014
Simmering Term 3
Multiplication 5
Session 1
Objective: Use the grid method to multiply two-digit numbers by two and
three-digit numbers (You may do this as two sessions not one.)
Teacher input with whole class
 Remind pupils how to use the grid method to multiply pairs of twodigit numbers. Using Grid method at
http://www.topmarks.co.uk/Flash.aspx?f=gridmethodpvcardsv3,
choose ‘TU × TU’, click on the place value cards to put them on the
grid, click on the question marks in the first row and then click on each
to add them. What have we found here? (98 × 30). Repeat for the
second row. What do we need to do next? Agree you need to add the
answers to 98 × 30 and 98 × 7 to find the answer to 98 × 37.

Repeat for a new set of numbers, first asking pupils to round each and
estimate the answer first.
Individual practice
 Pupils work in pairs to use the digits 2, 4, 6 and 8 to create two-digit by
two-digit multiplications. How many can they work out in five
minutes?
Teacher input with whole class
 Remind pupils how we can use the same methods to work out 527 ×
63, emphasising what products we are finding on each row before we
add them together.
Paired pupil work
 Pupils work in pairs to multiply 527 by four other two-digit numbers of
their choice, estimating the answer first each time.
HSNP © Hamilton 2014
Simmering Term 3
Multiplication 5
Session 2
Objective: Use a written method to multiply three and four-digit numbers
by single-digit numbers, incl. decimals (Only do this day if appropriate.)
Teacher input with whole class
 Remind pupils how they can use the grid method to keep track of the
partitioning when multiplying three-digit numbers by single-digit
numbers, e.g. 2764 × 3. Ask them to quickly work this out using grid
method. Show the following layout and discuss how the method is the
same, but the layout is different in order to make the addition easier:
2764
×3
6000
2100
180
12
8292
Paired pupil work
 Pupils work in pairs to work out 4526 × 6 and 7264 × 3. One person
uses the grid method and the other the vertical layout, then swap.
 They discuss the advantages and disadvantages of each layout.
Teacher input with whole class
 Take feedback. Check that pupils realise how important it is to align
the partial products to the right so that they add the correct digits
when using the ‘ladder’ method.
 Remind pupils how they can use the grid method to keep track of the
partitioning when multiplying four-digit numbers with two decimal
places by single-digit numbers, e.g. 74.68 × 3. If necessary remind
pupils that the answer to 3 × 0.6 is a tenth of the answer to 3 x 6 and
the answer to 3 × 0.08 is a hundredth of the answer to 3 × 8. Show
them how they can use the ladder layout.
 Pupils choose to use the grid method or ladder layout to work out:
45.7 × 6, 273.4 × 7, 42.41 × 7 and 72.35 × 4.
HSNP © Hamilton 2014
Simmering Term 3
Multiplication 5
Session 3
Objective: Multiply pairs of fractions
Teacher input with whole class
 Write 2/3 × 1/4 on the board. Draw a cake. Divide into ¼s. Then find 1/3
of that ¼ . Write 1/3 of ¼ is 1/12, and so 2/3 of ¼ is twice that, 2/12, which
simplifies to 1/6. Remind pupils that a quick way to multiply fractions is
to multiply the numerators and the denominators.
2×1
= 2 =1
3×4
12
6
 Discuss how we could also ‘cancel’ the 2 and the 4 to give 1 × 1 over 3
× 2. Point out that the answer is smaller than either of the fractions
being multiplied. If we have 2/3 of 1 /4 of pizza, we have a smaller piece
than 2/3 or 1/4, in fact a very small slice!
Paired pupil work
 Pupils work in pairs to remove the Jacks, Queens, Kings and Jokers
from a pack of playing cards, shuffle them and place in a pile face
down. They each turn over two cards to create a fraction, placing the
smaller card over the larger card. The first to multiply the two fractions
together wins all four cards. They carry on until there are no more
cards. Who won most cards?
Teacher input with whole class
 Write 7/5 × 4/3 on board, ask pupils to work this out and discuss what
they notice. The answer this time is not smaller than either fraction,
why? Agree that both fractions are greater than 1, and when multiply
numbers more than 1, the answer is greater than either number.
 Write 1 2/3 × 2 3/4 on the board. Remind pupils that a quick way to
work this out is to convert both mixed numbers to improper fractions,
find the product, and then convert back to a mixed number. Ask pupils
to do this, checking with a partner.
Paired pupil work
 Pupils play the game with playing cards again, but this time make
fractions in the order that they select cards, so some might be
improper fractions. Convert answer to a mixed number as required.
HSNP © Hamilton 2014
Simmering Term 3